ACM刷题之HDU————How Many Trees?

How Many Trees?

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 1225 Accepted Submission(s): 645 

Problem Description

A binary search tree is a binary tree with root k such that any node v reachable from its left has label (v) <label (k) and any node w reachable from its right has label (w) > label (k). It is a search structure which can find a node with label x in O(n log n) average time, where n is the size of the tree (number of vertices). 

Given a number n, can you tell how many different binary search trees may be constructed with a set of numbers of size n such that each element of the set will be associated to the label of exactly one node in a binary search tree? 

 

Input

The input will contain a number 1 <= i <= 100 per line representing the number of elements of the set.

 

Output

You have to print a line in the output for each entry with the answer to the previous question.

 

Sample Input

123

 

Sample Output

125

 

输入节点数。输出二叉树的可能性。

网上有公式： h(n ) = h(n-1)*(4*n-2) / (n+1)

用JAVA来做。

下面是ac代码:

import java.math.BigInteger;import java.util.Scanner;import java.math.*;import java.text.*;public class Main{public static void main(String[] args) {// TODO 自动生成的方法存根Scanner cin=new Scanner(System.in);int i=4;BigInteger[] big = new BigInteger[102];big[1] = new BigInteger("1");big[2] = new BigInteger("2");big[3] = new BigInteger("5");BigInteger n1 = new BigInteger("24");BigInteger n = new BigInteger("4");BigInteger cont = new BigInteger("4");BigInteger two = new BigInteger("2");BigInteger one = new BigInteger("1");BigInteger four = new BigInteger("4");for(i=4;i<101;i++){big[i]=big[i-1].multiply(four.multiply(cont).subtract(two)).divide(cont.add(one));cont=cont.add(one);}while(cin.hasNext())   //等同于!=EOF{i=cin.nextInt();System.out.println(big[i]);}}}